This invention relates to architectural framed structures and methods in general, and more particularly to ones having a coupled girder system capable of dissipating seismic energies.
Framed structures have been used for centuries in building construction. Most typically, they are in the form of a rigid frame, utilizing rigid couplings between columns and girders. Buildings in seismically active locations are likely to be subject to oscillatory (i.e., repeated back and forth) lateral forces or lateral shaking during an earthquake. The rigid frame forms a moment frame that provides a building with resistance to lateral forces by the stiffness of the columns and girders and the rigid connection between them.
FIG. 1 illustrates a cross-sectional view of a modern steel I-beam that is used to form columns and girders of a framed structure. The head and foot sections of the xe2x80x9cIxe2x80x9d is known as the xe2x80x9cflangesxe2x80x9d, and connecting them in between is the body section known as the xe2x80x9cwebxe2x80x9d. A steel I-beam comes in various dimensions as classified by the American Institute of Steel Construction. For example a W24 I-beam would be a wide flange rolled steel with a nominal depth of 24 inches from head to foot.
FIG. 2 illustrates a conventional framed structure formed by a lattice of columns and girders. One modern example of such a structure is the Special Moment Resisting Frame (xe2x80x9cSMRFxe2x80x9d). For simplicity only two columns and two girders are shown, even though in general the lattice formed is a three-dimensional one. In a framed structure, a girder is coupled to a column at an angle, typically at right angle, to form a rigid moment connection.
In the early part of the twentieth century, the I-beams were joined together using rivets that connected both the web as well as the flanges of the girder to the column. Angles or bent plates were used to transfer the forces from the girder flange to the column flanges. Later, with the advent of welding technology, the girder-to-column rigid moment connections were made utilizing the technique of welding the girder flange to the column flange. The girder webs were traditionally bolted using high strength bolts.
When a force is applied to a rigid material such as steel, there is a xe2x80x9cstressxe2x80x9d on the material which results in a displacement or xe2x80x9cstrainxe2x80x9d. The characteristics of steel ante such that the stress-strain relation is initially in a linear or (xe2x80x9celasticxe2x80x9d) regime where the strain is proportional to the stress. Furthermore, the process is reversible in that the strain is reduced in proportion with the stress by retracing the linear relation. Since, energy is given by integrating the applied force over the displacement, it is equivalent to the area under the stress-strain curve. In the elastic regime, as force is applied, energy is stored in the rigid material, but when the force is removed, the energy stored as strain energy is translated into kinetic energy (i.e., movement of the frame). Thus, there is no dissipation or removal of energy from the material.
On the other hand, when the stress exceeds a certain value for a given material where the resulting strain is beyond a certain point called the xe2x80x9cyieldxe2x80x9d point, the material enters into a regime where it starts to yield inelastically. Here, the stress-strain relation begins to deviate from a linear relation. More importantly, in the inelastic regime the process is irreversible in that the stress-strain curve is not retraced as the stress is subsequently decreased. Thus, in the inelastic regime the energy stored in the material is dissipated as heat instead of kinetic energy during the yielding of the material. Since the heat escapes to the outside environment, this energy is then permanently lost from the material which allows the motions to die out. This phenomenon is called xe2x80x9cdampingxe2x80x9d.
FIGS. 3A-3C illustrates schematically the behavior of a simple conventional framed structure in response to lateral forces. FIG. 3A is a schematic representation of a simple conventional framed structure formed by a girder supported by two columns. FIG. 3B illustrates schematically the deformation to the conventional framed structure of FIG. 3A in response to a force from left to right. The moment frame rotates clockwise resulting in a deformation of the girder which tries to maintain at right angle at the joints to the columns. The stress and strain in the girder is flexural in nature without any net load along the long axis of the girder (axial load). At the right end of the girder, the stress in the top half portion is compressive and the stress in the bottom halfportion is tensile. At the left end of the girder, the reverse is the case. Similarly, FIG. 3C illustrates schematically the deformation to the conventional framed structure of FIG. 3A in response to a force from right to left.
When the drift is below a predetermined value for a given structure, the strain is in the elastic regime and the energy stored is returned when the stress is removed in the form of reverse movement of the frame (i.e., kinetic energy).
However, when the drift exceeds the predetermined value, the girder begins to yield inelastically and energy is dissipated as heat while the material changes character by becoming hardened. After repeated cycles of post-yield stresses the material is ultimately susceptible to rupture. In major earthquakes (DBE), it has been observed that there are only two or three cycles of the highest magnitude which will likely push a structure to go into inelastic yielding.
In the case of the welded joints, it was assumed, based on a limited number of tests, that the welded connection will be stronger than the parent metal. In the event of large earthquakes, the steel in the girder will yield inelastically and thus absorb energy and provide damping to the structure. The 1990 Northridge Earthquake in Southern Calif., USA and a short time later the Kobe Earthquake in Japan have showed the assumed ductility (i.e., ability for the frame to continue displacing after the girder column joint had reached the yield point in steel and thus absorb energy) was not achieved in a large number of joints. This led to further research and new connection joints were developed. However, even after a good deal of testing, only a few type of joints have been tested and confirmed to have sufficient ductility that is required to absorb energy from the earthquakes by the inelastic rotation of the joint. During the inelastic rotation of the joint, the girder behaves in a flexural manner by bending slightly near the joints. One type of joint that is now considered desirable is one where the girder incorporates a weaker spot at each end near but slightly away from the joint. This weak spot is known as Reduced Beam Section (xe2x80x9cRBSxe2x80x9d), also known as xe2x80x9cdog bonexe2x80x9d. The incorporation of RBS in the girder allows better control of the yielding of the girder away from the region of material that may have been modified by the formation of a joint and its welding.
Two seismic design criteria have been established by the structural engineering profession. The Design Basis Earthquake (xe2x80x9cDBExe2x80x9d) is defined in statistical terms as an earthquake event that has less than 10% likelihood of being exceeded in the economic life of the structure, deemed for most civil structures as 50 years. On the other hand, the Maximum Capable Earthquake (xe2x80x9cMCExe2x80x9d) is defined as an event that has less than 10% likelihood of being exceeded in 100 years. Beyond these two design criteria, there are no defined expectations for most structures except the overall goal is to prevent collapse.
It has been established in building practices that a building should be sufficiently stiff not to suffer more that 0.3% to 0.6% drift elastically. In terms of the moment frame, it approximately translates to 0.2% rotation in the elastic regime. This will prevent the building from straying uncomfortably under wind loads and to recover after mild to moderate earthquakes.
Moreover, the columns and girders of a moment frame should be proportioned such that in the event of an earthquake, it enters into the inelastic regime beyond a predetermined amount of rotation. When the DBE design goal is applied to a moment frame, the rotation in the girder at the column joint for the onset of inelastic yielding has been predetermined to be 3%. This allows the structure to translate laterally approximately in the 1.5% range in addition to the 0.3% to 0.6% range allowed for the elastic case. This range of approximately 2% total structure drift is regarded in the structural engineering profession as acceptable in the event of a large earthquake such as that of a DBE.
In most buildings used for commercial purposes, such as office buildings, the floor-to-floor height is usually between 13 feet and 14 feet. The exterior of the building usually has a glass window that is 7 feet in height. Thus, there exists a space of approximately 6 to 7 feet vertically for the girder to be fit in the perimeter moment frames. Also, in the core of the structure a similar height is available. In hospitals, convention centers and other special use buildings, story heights are typically 18 feet or greater, which allow a even larger space for girders in each story. The moment frames normally have a column spacing that varies from 20 to 40 feet. Thus, the girder length is usually 1.5 times to 3 times the length of the columns. In the traditional older structures, W14 columns were used and they matched the stiffness of the deeper girders, usually in the range of W24 to W36 members. These columns were used for moment connections in the two orthogonal directions for what is called a xe2x80x9ctwo way moment framexe2x80x9d system.
Since the early 1960s, wider shape columns, i.e., W24 to W36 series in rolled shapes, have been introduced in buildings. The same types of I-beams are also being used for the girders in a perimeter frame to reduce tonnage of steel for the building frames. Today, these shapes are used by many engineers in even single frames, without using the full perimeter frame. Used in this way, the shorter column lengths have larger stiffness than the girders of similar depth.
Generally, two considerations enter into the design of a moment frame. The first consideration is the stiffness ratio between column and girder, which is related to efficiency and economy. The second consideration is the strength ratio between column and girder, which is related to desired behavior in the event of an earthquake. These two considerations are somewhat in conflict with each other.
It has been established that a girder to column stiffness ratio of unity is efficient, i.e., it reduces the total tonnage of steel used in the frames since the frames are generally governed by the elastic stiffness requirements of building codes for lateral loads and not by the state of stress. However, use of deeper girders, which will accomplish the goal of a stiffness ratio of unity between girders and columns, also leads to making the girders stronger than the columns. Since in taller buildings, the column shape selected is often W36, which is near to the maximum depth of rolled shapes, girders will need to be plate-fabricated to shapes of greater depths which add significantly to cost. A deeper girder will be stronger than the column. A girder stronger than the column is undesirable in the behavior of the frame as it can lead to individual story collapse in an earthquake. Building codes therefore expressly forbid the use of a strong girder with a weak column in buildings that rely on the rigid frames to resist earthquakes.
While a conventional frame structure using a single girder per floor level does provide some degree of seismic dissipation by the mechanism of flexural inelastic yielding, there is always the desire to have structures with even better dissipation of seismic energy which are also economic to build and have high performance.
It is therefore a general object of the invention to provide an improved framed structure and method therefor capable of enhanced dissipation of seismic energy.
It is another general object of the invention to provide an improved framed structure and method therefor that are economical and high performance.
It is an object of the invention to provide an improved framed structure that offer improved dissipation of seismic energy and yet is relatively stiff and light weight.
It is an object of the invention to provide an improved framed structure and method therefor that are easy to fabricate and assemble.
It is another object of the invention to provide an improved framed structure and method therefor that allows easy post-earthquake inspection and assessment of damage.
It is another object of the invention to provide an improved framed structure and method therefor that allows easy post-earthquake repair of damage in the framed structure.
These and other objects of the invention are accomplished briefly by having a rigid framed structure that incorporates the Coupled Girder Moment Resisting System (xe2x80x9cCGMRSxe2x80x9d) of the invention. Such a framed structure includes at least a pair of spaced-apart girders supported by a pair of adjacent columns. The pair of spaced-apart girders are coupled by at least one, and preferably two girder-to-girder links such that when a drift develops in response to seismic energy input to the rigid frame structure, and when said drift exceeds an elastic limit, each of the girder-to-girder links yields inelastically to dissipate substantial portion of the seismic energy.
Various preferred embodiments ensure the integrity and stability of the girder-to-girder links and girders under yielding stress so that the girder-to-girder links can perform its energy dissipation function as intended.
CGMRS solves the problems of a) poor performance of the frame joints, b) girder stiffness deficiency and c) energy dissipation deficiency. It provides a higher level of redundancy, a concept desirable in the reliability of the earthquake resisting systems. Redundancy in building structure implies greater number of elements resisting the loads such as earthquake (or seismic) loads so that the likelihood of failure of the structure as a whole in each story of the building is reduced simply by the multiplicity of resisting elements.
In the elastic stage of drift of the structure, 5% damping is generally available. In the inelastic stage of drift, 20% damping is generally attained at 1.5% inelastic rotation of the girders due to flexural yielding.
By having the girder-to-girder links yielding earlier, the CGMRS provides an additional 3% to 5% damping to the structure provided by the damping from the conventional flexural yielding of the girders. This is in addition to the about 5% to 20% damping described earlier. Thus, by enabling yielding from the girder-to-girder links in the early stages of the inelastic behavior of the structure during a major earthquake, the demand on the balance of the structure is reduced. Thus, damage to the structure can be controlled such that the links provide added safety to the structure.
The vertical links can be relatively inexpensively repaired, both due to easier access, i.e., the vertical links are not covered by the floor concrete such as is the case of the girder top flange, as well as because the vertical links are connected to girders using simpler and smaller connections. In addition, the repair of the girder-to-girder links or vertical links will not involve applying heat to the columns nor require shoring of the girder in most cases.
Since the links are also providing additional stiffness and strength, the added damping makes it possible to have a lighter, stronger and more damage resistant frame than the conventional single girder frames or a coupled girder that is designed only for the stiffness and strength.
Additional objects, features and advantages of the present invention will be understood from the following description of its preferred embodiments, which description should be taken in conjunction with the accompanying drawings.